Questions on Algebra: Exponent and logarithm as functions of power answered by real tutors!

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Question 1105182: If 64^2n+1 = 16^4n-1, what is the value of n?
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Question 1105188: If n is a negative integers, which statement is always true?
a) 6n^-2 <4n^-1
b) n/4 > -6n^-1
c) 6n^-1 < 4n^-1
d) 4n^-1 > (6n)^-1

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Question 1105185: If, x^3 = -27/125 then x^2 = ?
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Question 1105186: A species of bacteria doubles every 2 hours, so that a culture of 200 bacteria would grow to 400 after 2 hours and 800 after 4 hours. If there were b bacteria initially, which of the following expressions correctly describes the amount of bacteria present after one day?
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Question 1105174: If x^1/2 = 1/8, what is the value of x^2/3?
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Question 1105180: If a, b, and c are positive numbers such that √a/√b = 8c and ac = b what is the value of c?
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Question 1105173: square root of (3p^2 - 11) - x = 0
If p > 0 and x = 8 in the equation above, what is the value of p?

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Question 1105173: square root of (3p^2 - 11) - x = 0
If p > 0 and x = 8 in the equation above, what is the value of p?

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Question 1105181: If k = 8√2 and 1/2k = √3h, what is the value of h?
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Question 1105184: A meteorologist estimates how long a passing storm will last by using the function t(d) = 0.08d^3/2, where d is the diameter of the storm, in miles, and t is the time, in hours. If the storm lasts 16.2 minutes, find its diameter, in miles.
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Question 1105176: If y is not equal to 0, what is the value of 6(2y)^-2 / (3y)^-2 ?
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Question 1105177: If (2rs)^-1 = 3s^-2, what is the value of r/s ?
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Question 1105177: If (2rs)^-1 = 3s^-2, what is the value of r/s ?
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Question 1105179: If m and p are positive integers and (2√2)^m = 32^p, what is the value of p/m ?
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Question 1105183: Third root of a^8 / (√a)^3 = a^x , where a > 1
In the equation above, what is the value of x?

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Question 1105269: Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros: 3, (i square root of 2)
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Question 1105275: Hi! I came across this problem in a CLEP practice test, and I'd never had any experience with it before. I'm not exactly sure how to look for tutorials because I don't know what this particular kind of problem is called. Here it is: If ln(√x) = 5 and ln(y3) = 3, what is ln(x2y)? Can you help me learn how to solve this? Thank you!

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Question 1104940: X -4, -3, 0, 1, 3,
f(x) -2, -5, __, -9, __,
g(x) 1, 7, -4, __, __,
(f-g) __, -12, __, -13, -5,
(f/g)(x) -2, __, 3/2, __, 7/2,

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Question 1105288: If the two roots of the quadratic equation x^2-6x+1=0 are log a and log b,
what is the value of log(a,ab^2)+log(b,a^2b)?
Thank You.

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Question 1104551: Please help me solve this word problem:
in 1991, the average cost of attending a public university through graduation. Was $20,972. If johns parents deposited that amount in an account in 1991 at an interest rate of 7% compounded semi-annually, how long will it take for the money to double? Round answer to two decimals.

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Question 1104551: Please help me solve this word problem:
in 1991, the average cost of attending a public university through graduation. Was $20,972. If johns parents deposited that amount in an account in 1991 at an interest rate of 7% compounded semi-annually, how long will it take for the money to double? Round answer to two decimals.

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Question 1104553: Please help me solve this word problem:
The number of households using online banking services has increased from 754,000 in 1995 to 12,980,000 in 2000. The formula H(t)=0.76e^0.55t models the number of households H in millions when time is t years since 1995. In what year was it estimated that 50,000,000 households would use online banking services?

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Question 1105705: If, (b/a)^n=a, then what is the answer to (b/a)^x=b
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Question 1105952: SOLUTION: 1. Write an Assembler Program using the Emu8086 that will input a string of lower case letters from the keyboard, store the string in memory, and then display the equivalent UPPE

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Question 1106166: In 2011, Julie will be the same age as the square of her age in 2005. How old is Julie in 2008?
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Question 1106166: In 2011, Julie will be the same age as the square of her age in 2005. How old is Julie in 2008?
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Question 1106165: Johnny has x rows of boxes, each row containing another x boxes. If the number of boxes Johnny has is equal to one-fifth of the number of boxes that Kelsey has, what is the value of x when Kelsey has 1280 boxes?
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Question 1106164: the cube root of 8x^3
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Question 1106248: Rewrite in base 10.
log (6) 72
Thanks! Show steps please, I'm not sure how to do this one.

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Question 1106247: Rewrite the following in base e.
Log (2) 64

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Question 1106244: Solve for t algebraically. Round answers to the nearest hundredth.
100(1/2)^t/5 = 20
So,I know you divide the whole equation by 100,which leaves me with,
(1/2)^t/5 = 1/5
Then I take the log of each side, my book tells me to use ln, so I end up with
ln(1/2)^t/5 = ln 1/5
Move t/5 over, now I get
t/5 ln(1/2) = ln 1/5
Multiply everything by 5
t ln(1/2) = 5 ln 1/5
Is that correct? I've tried everything I can think of, yet I still get the wrong answer. Would you please help me?

Click here to see answer by Alan3354(69443) About Me 

Question 1106245: IF Annabelle invests $200 at 3% interest rate for t years, she will have the amount A= 200(1.03)^t dollars. How many whole years must Annabelle wait for the amount to reach 500? So,obviously I plug in 500 as A,and I end up with,
500=200(1.03)^t
Divide by 200
2.5=1.03^t
So,er...what now?

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Question 1106332: 2ln(100-3x)-8=0.5
Round answer to nearest thousandth,solve for x.

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Question 1106341: 4^(x+1)=23
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Question 1106349: 1+2logx
Express as the log of a single quantity.

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Question 1106349: 1+2logx
Express as the log of a single quantity.

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Question 1106346: Solve for t.
3000(1-e^(-2t))=1,200
So,I know you divide everything by 3000,right?
1-e^(-2t)=2/5
Now what do I do?

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Question 1106344: log↓4(x^2 + 3x)-log↓4(x+5)=1
Please show me how to do it

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Question 1106348: log↓2(x-4)+log↓2(x)=5
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Question 1106347: log↓3(x)=2.5
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Question 1106347: log↓3(x)=2.5
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Question 1106347: log↓3(x)=2.5
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Question 1106345: 4^(x+1)=23
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Question 1106336: Simplify.
log 10^(2x-1)

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Question 1106343: A scientist has 10 grams of a radioactive substance with a half-life of 8 days. The formula A = 10(0.5)^(t/8) tells how much will be left after t days. How many days, to the nearest tenth,will it take until only 1 gram is left?
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